June 11, 2014

Overthinking It

The OTHER Way We Could Move the Mound

by Ben Lindbergh

Even if you’ve missed Rob Neyer’s midnight ride to warn the world about the Strikeout Scourge—one if by land, two if by sea, three strikes you’re out—you can’t help but have noticed how many plate appearances are ending in punchouts. Baseball’s strikeout rate is up this season (from an old-record 19.9 percent last year to a new-record 20.4 percent in 2014), and batting average is at its lowest ebb in the DH era. As a result, action seems scarce, unless you prefer seeing swings-and-misses to watching balls in play.

Everyone has a pet fix for this state of affairs, or at least a way to prevent it from growing worse. Although recent research by Russell Carleton revealed that educating hitters might help turn the tide, most proposed solutions suggest hamstringing hurlers. Tighten the strike zone. Limit the number of permissible pitching changes. Politely ask Stephen Strasburg to retire for the good of the game.

Last month, Tom Verducci became the latest to speak out in favor of another measure that would, quite literally, take pitchers down a peg: lowering the mound. Because it’s been done before, and within living memory, the idea has the virtue of being an easier sell than some of the alternatives. We also know it would work, although the effect on strikeouts wouldn’t necessarily be dramatic. When the (then 15-inch) mound was introduced in 1904, the league strikeout rate rose only from 9.8 percent to 10.4 percent, though the batting average fell from .262 to .247. When the mound shrank from 15 inches to its current height of 10 inches in 1969, the strikeout rate again barely budged, from 15.8 percent to 15.2, and the batting average rose from .237 to .248. The real offensive revival had to wait for Ron Blomberg (just as the next one might have to wait for his National League equivalent).

Verducci argued that lowering the mound would also address another big baseball scourge, pitcher elbow injuries, by reducing stress during the delivery. If true, that would be a compelling point in its favor. However, Verducci’s article offers no data to support that position. A study from 2007 supplied some evidence, but it was based on a small, low-stakes sample and “did not result in enough data to recommend reducing the 10-inch mound height.” The alleged link between mound height and elbow problems has since been contradicted by the American Sports Medicine Institute, which called the notion that lowering or removing the mound would reduce stress on the elbow and reduce UCL injuries a “common misconception.” According to ASMI, “elbow torques during full-effort pitching on a mound a full-effort throwing on flat ground are about the same.”*

So let’s ignore injuries, which may or may not have much to do with the mound, and tackle one scourge at a time. Even in the category of mound-related strikeout solutions, is lowering the rubber the best we can do?

Baseball is unusual, if not unique, among sports in its laissez-faire approach to the layout of the field. Vital variables such as wall distance, wall height, playing surface, and the size of foul territory vary by ballpark, and no one bats an eye. Yet baseball also prizes itself on the perfection of the few aspects of the field that are strictly regulated. Many, for instance, regard the 90-foot distance between bases as sacred, a rare triumph of intelligent design over evolution. (If fossilized 85- or 95-foot baselines are out there, we haven’t found them.) Sportswriter Red Smith, in his understated way, called the baselines “man’s closest approach to absolute truth” and “one of the few examples of perfection on earth.”

The distance from the pitcher’s mound to home plate, however—60 feet, six inches—inspires no such sentimentality. Fractional feet? Come on. The mound is almost begging to be moved.

Of course, the mound (or what once passed for one) has been moved back before, albeit not as recently as it was last lowered. In 1881, the minimum pitching distance was extended from 45 to 50 feet, in an attempt to “increase the batting.” The attempt succeeded: The strikeout rate fell from 7.9 percent to 7.0 percent, and batters gained 15 points of batting average, 23 points of on-base percentage, and 18 points of slugging. However, that was before pitchers were permitted to throw overhand, a right they gained in 1884. Overhand pitching significantly decreased the batting, to the tune of a 45 percent bump in strikeout rate, a 14-point decrease in batting average, and a 25-point difference in OPS.

That meant more adjustments. In 1887, a “pitcher’s box” was created, with its front border remaining 50 feet from the plate but its back border—where the pitcher was required to keep his back foot—5 ½ feet farther away. This time, the impact was obvious: The strikeout rate fell by 37 percent, and batting average rose by 25 points, with a 71-point increase in OPS. Another five-foot move in 1893, which pushed pitchers back to their current distance, produced another large shift: a 38 percent decrease in strikeout rate, a 35-point gain in batting average, and a 92-point inflation of OPS. Since then, pitchers have grown considerably taller, which translates to longer strides, longer arms, and release points closer to home plate, but the mound hasn’t moved back to compensate.

If we assume that the effect of distance on strikeout rate is linear, then we can say that every foot by which the pitching area shifted in 1887 and 1893 reduced the K rate by 7.5 percent. It’s probably dubious to apply 19th-century results to 2014, but let’s do it anyway! If the same relationship held true, moving the mound back to 65 ½ feet would send today’s strikeout rate back to where it was, on average, from 1975–82. That sound you just heard was Rob Neyer sobbing with joy.

You want to see some math, right? Of course you do. I did, too, so I asked BP contributor Alan M. Nathan, a physics of baseball researcher and Professor Emeritus of Physics at the University of Illinois at Urbana-Champaign, to weigh in. Here’s how he calculated the increase in flight time—and even more importantly, the increase in the amount of time the batter has to react to the pitch.

Suppose a ball is released a distance Y from home plate at speed V and it takes a time T to get to home plate. Now compare with a pitch released at speed V1 at 55 ft that takes the same time T to get to home plate. Then V1=V*55/Y. For example, suppose the mound is moved back a whopping 5 ft, so that Y is 60. The V1 (the "perceived velocity") is V*55/60, so that a fastball released at 95 mph "looks like" only 87 mph, in the sense that flight time is the same as a pitch released at 55 ft at 87 mph. That's a very big effect, corresponding to a ~10% increase in flight time, or about 40 ms. And it's even [more dramatic] than that in that the amount of time the batter has to observe the pitch is, say, only about half the flight time, or about 200 ms. Now add 40 ms on to that and you get a 20% effect. Huge!

As Robert K. Adair writes in The Physics of Baseball (and as this image makes clear), “the player cannot begin ‘thinking’ about an observation until 75 milliseconds after the time it occurs. Similarly, the muscles cannot begin an action until 25 milliseconds after the thinking process in the brain orders that action.” Thus, he concludes, “none of the subsequent information from seeing the ball over the last half of its flight can be used at all.” The takeaway, Nathan says, is that “an x% increase in flight time (by moving the mound back) really amounts to more like a 2x% change in useful observation time,” though that varies by batter to a certain extent.

Major League Baseball couldn’t make a change like this lightly, since it would likely have some unintended consequences. To get a sense of what those might be, I asked former big-league pitcher Brian Bannister for his thoughts.

“You don’t want to get into a scenario where pitchers have to purposely angle their pitches upwards in order to get them there,” Bannister says. “I don’t know what that distance would be, but it would probably feel like slow pitch softball if it was too far.”

As it turns out, Nathan can calculate that, too. Here are his findings about the impact of moving the mound on the pitcher’s vertical launch angle:

I wanted to compare a 95 mph fastball (FA) with a 85 mph changeup (CH). I asssumed a release point at either 55 or 60 ft. I fixed the vertical release point at 6 ft. I then investigate the range of vertical launch angles such that the ball ends up in the strike zone, which I took to be 1.75-3.40 ft. Here are the results:

55 ft, FA: -1.9:-3.7 CH: -1.3:-3.1
60 ft, FA: -1.6:-3.3 CH: -1.0:-2.6

Some comments. First, the range of launch angles is smaller for both pitches at the larger distance. That makes sense to me: You have to "aim better" to get the ball in the strike zone if you move farther away. Second, the range of angles is more or less the same for FA and CH, whether at 55 or at 60 ft. In both cases, the range of launch angles is shifted upward for CH relative to FA by about 0.6 deg. Third, for both release points, there is a greater downward angle for FA than for CH, which makes complete sense to me, since the slower pitch will drop more.

Not only is the effective velocity of the pitch reduced when it’s released from farther back, but the pitcher’s accuracy suffers also. Bannister adds that it would be more difficult for pitchers to field bunts and dribblers from farther away, though he also notes that right-handed pitchers would be able to keep a closer eye on runners on first. It’s hard to say whether shrinking the mound or moving it back would force pitchers to make more mechanical adjustments or feel like they had to overthrow in a way that would jeopardize their arms, though he noted on the Effectively Wild “Rising Strikeout Rate Symposium” that “Most guys hate throwing off a flat mound, just because they feel like it destroys what they’re trying to do.”

Considering all of the above, pushing the mound back by five feet might have a greater effect than we’d want, but there’s no need to be that aggressive from the get-go. “Moving things back by a smaller amount, say two feet, might be something to consider,” Nathan says. Visually, a move that minor would be difficult for fans to detect from home or from the stands, but the decrease in strikeouts and increase in scoring would stand out.

If we’re going to alter the mound in some fashion to curtail the K's, we might want to do what our baseball forebears did during the Victorian era, which worked well enough. The baseball diamond exists in three dimensions, so up and down aren’t the only options. Let’s really explore the space.

*“From a pitcher’s perspective, one of the interesting things about pitching off of a lower mound is that you tend to get more sore afterwards,” Bannister says.

Thanks to Rob McQuown for research assistance.

Ben Lindbergh is an author of Baseball Prospectus. Follow @benlindbergh
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